Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Randomized quasi-Monte Carlo simulation of fast-ion thermalization
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.ORCID iD: 0000-0002-7142-7103
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
2012 (English)In: Computational Science & Discovery, ISSN 1749-4680, E-ISSN 1749-4699, Vol. 5, no 1, 014010- p.Article in journal (Refereed) Published
Abstract [en]

This work investigates the applicability of the randomized quasi-Monte Carlo method for simulation of fast-ion thermalization processes in fusion plasmas, e.g. for simulation of neutral beam injection and radio frequency heating. In contrast to the standard Monte Carlo method, the quasi-Monte Carlo method uses deterministic numbers instead of pseudo-random numbers and has a statistical weak convergence close to O(N -1), where N is the number of markers. We have compared different quasi-Monte Carlo methods for a neutral beam injection scenario, which is solved by many realizations of the associated stochastic differential equation, discretized with the Euler-Maruyama scheme. The statistical convergence of the methods is measured for time steps up to 2 14.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2012. Vol. 5, no 1, 014010- p.
Keyword [en]
Monte Carlo, quasi-Monte Carlo, low discrepancy sequence, variance reduction
National Category
Fusion, Plasma and Space Physics
Identifiers
URN: urn:nbn:se:kth:diva-91197DOI: 10.1088/1749-4699/5/1/014010Scopus ID: 2-s2.0-84866342521OAI: oai:DiVA.org:kth-91197DiVA: diva2:508790
Note

QC 20121114. Updated from submitted to published.

Available from: 2012-03-13 Created: 2012-03-09 Last updated: 2017-12-07Bibliographically approved
In thesis
1. Variance reduction methods for numerical solution of plasma kinetic diffusion
Open this publication in new window or tab >>Variance reduction methods for numerical solution of plasma kinetic diffusion
2012 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Performing detailed simulations of plasma kinetic diffusion is a challenging task and currently requires the largest computational facilities in the world. The reason for this is that, the physics in a confined heated plasma occur on a broad range of temporal and spatial scales. It is therefore of interest to improve the computational algorithms together with the development of more powerful computational resources. Kinetic diffusion processes in plasmas are commonly simulated with the Monte Carlo method, where a discrete set of particles are sampled from a distribution function and advanced in a Lagrangian frame according to a set of stochastic differential equations. The Monte Carlo method introduces computational error in the form of statistical random noise produced by a finite number of particles (or markers) N and the error scales as αNβ where β = 1/2 for the standard Monte Carlo method. This requires a large number of simulated particles in order to obtain a sufficiently low numerical noise level. Therefore it is essential to use techniques that reduce the numerical noise. Such methods are commonly called variance reduction methods. In this thesis, we have developed new variance reduction methods with application to plasma kinetic diffusion. The methods are suitable for simulation of RF-heating and transport, but are not limited to these types of problems. We have derived a novel variance reduction method that minimizes the number of required particles from an optimization model. This implicitly reduces the variance when calculating the expected value of the distribution, since for a fixed error the  optimization model ensures that a minimal number of particles are needed. Techniques that reduce the noise by improving the order of convergence, have also been considered. Two different methods have been tested on a neutral beam injection scenario. The methods are the scrambled Brownian bridge method and a method here called the sorting and mixing method of L´ecot and Khettabi[1999]. Both methods converge faster than the standard Monte Carlo method for modest number of time steps, but fail to converge correctly for large number of time steps, a range required for detailed plasma kinetic simulations. Different techniques are discussed that have the potential of improving the convergence to this range of time steps.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. viii, 42 p.
Series
Trita-EE, ISSN 1653-5146 ; 2012:007
Keyword
variance reduction, Monte Carlo, quasi-Monte Carlo, kinetic diffusion, stochastic differential equation
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-91332 (URN)978-91-7501-278-0 (ISBN)
Presentation
2012-03-30, Seminarierummet, Teknikringen 31, KTH, Stockholm, 12:24 (English)
Opponent
Supervisors
Note
QC 20120314Available from: 2012-03-14 Created: 2012-03-13 Last updated: 2012-03-14Bibliographically approved
2. Numerical solution of quasilinear kinetic diffusion equations in toroidal plasmas
Open this publication in new window or tab >>Numerical solution of quasilinear kinetic diffusion equations in toroidal plasmas
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

One of the main challenges for the realization of a working fusion power plant is an increased detailed understanding of kinetic phenomena in toroidal plasmas. The tokamak is a toroidal, magnetically confined plasma device and is currently the main line towards a power plant. The spatial and temporal scales in a tokamak plasma are extreme and the only tractable path for quantitative studies is to rely on computer simulations. Present day simulation codes can resolve only some of these scales. Nevertheless they still require the largest high performance computing (HPC) resources available in the world. In combination with the increase of computational performance, it is therefore necessary to improve the numerical algorithms used in the simulations.

In this thesis we have developed new numerical methods designed for Monte Carlo simulation of plasma kinetic diffusion. Examples are simulation of fast-ion thermalization and radio-frequency heating. The aim has been to reduce the statistical random noise in particle codes, produced by a finite number of particles (or markers). Traditionally the statistical noise is improved by increasing the number of particles (N) or by simulating the perturbation of the distribution (with particles) from a known distribution function. This is the well known δf method. In this thesis we have developed a new type of δf method, which minimizes the number of particles used in a simulation. The computational speedup of the new method is substantial. In this thesis, we have further benchmarked quasi-Monte Carlo techniques that improve the convergence rate from N−1/2 to N−1 for some cases.

In Monte Carlo simulations, error appears also from the time step discretization. Based on the mathematics of operator splitting, a new scheme for the pitch-angle scattering diffusion process has been developed that outperforms the standard methods. Finally this thesis also presents a new code, SELFO-light, for self-consistent simulations of ion cyclotron resonance heating, suitable for routine calculations, which couples a one dimensional Fokker-Planck model with the finite element wave solver LION.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. xiii, 54 p.
Series
Trita-EE, ISSN 1653-5146 ; 2013:012
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-120345 (URN)978-91-7501-697-9 (ISBN)
Public defence
2013-04-26, F3, Lindstedtsvägen 26, KTH, Stockholm, 13:15 (English)
Opponent
Supervisors
Note

QC 20130405

Available from: 2013-04-05 Created: 2013-04-04 Last updated: 2013-04-05Bibliographically approved

Open Access in DiVA

rqmc_fast_ion.pdf(1019 kB)322 downloads
File information
File name FULLTEXT01.pdfFile size 1019 kBChecksum SHA-512
2ec24d76e17e1297f0c8ab5e1e192c45ba7921620d009eda8f3081e0fab7f13b34c7fa13556b6c4976a1f7e3692a9a7674182a6b81f2215ab25de0f98526480c
Type fulltextMimetype application/pdf

Other links

Publisher's full textScopus

Authority records BETA

Johnson, Thomas

Search in DiVA

By author/editor
Höök, Lars JosefJohnson, ThomasHellsten, Torbjörn
By organisation
Fusion Plasma Physics
In the same journal
Computational Science & Discovery
Fusion, Plasma and Space Physics

Search outside of DiVA

GoogleGoogle Scholar
Total: 322 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 159 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf